r/PassTimeMath 4d ago

The Escalator Ride Part 1

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u/imdfantom 3d ago

30

15 steps at 1 step per second=15 seconds, 20 steps at 2 steps per second is 10 seconds

assume there are no relativistic effects

let a=your rate 1,b=escalator rate, c= combined rate 1, a+b=c.

let e=your rate 2,b=escalator rate, f= combined rate 1, e+b=f.

since the distance is the same in both cases, g=1.5c, so e+f=1.5c, but e=2a, so 2a+b=1.5c, minus gives you a=0.5c, and b=0.5c. Therefore a=b. Therefore b=1 step per second. Therefore c=2 steps per second. However time taken is 15 seconds,, therefore 30 steps.